Here in the UK, it's flipping cold at the moment. Walking back from a night out the other day, I realised that my skin had gone so dry that it was starting to crack. Knowing that every girl carries moisturiser (eg. Vaseline) with her, I was sure that there was some way to get some good kino out of this. Here's the best I've come up with so far (NB. obviously don't do this if your hands are manky):

"Hey, this is really embarrassing, but have you got any moisturiser? My hand goes all manky if I don't keep it moisturised."
*hold out right hand*
"Hold on, is that [name of product]? Damn, my left hand's allergic to that. You're going to have to rub it in for me"

Any ideas about this? I'll field test it tonight.

I'm not sure girls would respond well to you descibing your hand as going 'manky', surely girls might be put off by that, and may be nervous about catching some form of hand fungus off you. maybe if you just said 'my skin is getting dry in this cold' she might be a bit less alarmed.
Also I'v never known anyone have one hand allergic to something and not the other, she might call you out on that... but if you make it clear its a joke, and your only telling her this to get her to do it she might want to... but i think you'd have to have already made her comfortable with you before you do it.... so maybe a routine that would work better on someone you know.

personallly i'd still prefer the 'can you rub sun tan lotion into my back' its a bit more sexual, and a bit less 'manky'.

Noted.
Utterly ridiculous, I know, but I was hoping that someone else could come up with a better idea!
Look a little strange though when it's a) dark, and b) freezing!